The dynamics of the eddy shedding by the Loop Current in the Gulf of Mexico have been investigated using three nonlinear numerical models: two-layer, barotropic and reduced gravity. The barotropic and reduced gravity models demonstrate the individual behavior of the external and internal modes, and provide insight into how they interact in the two-layer model. Because of the economy of the semi-implicit free surface models, it was possible to perform over 100 experiments to investigate the stability properties of the Loop Current. Typically, the models were integrated 3–5 years to statistical equilibrium on a 1600 km×900 km rectangular domain with a resolution of 20 km×18.75 km. Prescribed inflow through the model Yucatan Channel was compensated by outflow through the Florida Straits.
A long-standing hypothesis is that the Loop Current sheds eddies in response to quasi-annual variations in the inflow. We find that the Loop Current can penetrate into the Gulf, bend westward, and shed realistic anticyclonic eddies at almost an annual frequency with no time variation in the inflow. In this regime, the eddy-shedding rate depends on the internal Rossby wave speed, an eddy diameter derived from conservation of potential vorticity on a β-plane, the angle of the inflow, and to a lesser extent on the Reynolds number. Eddy shedding can be prevented by reducing the Reynolds number sufficiently. However, the Loop Current still spreads far westward. The steady-state solution for a highly viscous case was found to be almost the same as the mean over an eddy cycle for a lower viscosity case which shed discrete eddies of large amplitude. Eddy shedding and westward spreading of the Loop can be prevented at higher Reynolds numbers when the beta Rossby number RB = vc/(βLp2) > 2, where the appropriate length scale Lp is one-half the port separation distance and vc is the velocity at the core of the current. Differential rotation (β) is also of great importance in determining the diameter and westward speed of the eddies and the penetration of the Loop Current into the Gulf. In a few of the two-layer experiments, baroclinic and mixed instabilities were encountered, but experiments dominated by a horizontal shear instability of the internal mode produced the most realistic results. For sufficiently high Reynolds numbers the shear instability occurred in both the barotropic and reduced gravity models. However, for realistic parameter values eddy shedding occurred in the two-layer and reduced gravity models, but not in the barotropic model.
Consistent with potential vorticity conservation dynamics, the Loop Current and its eddy shedding behavior were quite insensitive to the location and width of the inflow and outflow ports, so long as the western boundary did not interfere with the shedding process and the ports were not separated by much less than 1/???? times a theoretical eddy diameter, i.e., when RB < 2. When the entire eastern boundary was opened, the outflow remained confined to a current adjacent to the southern boundary. Also, while the solution depends on the maximum velocity at inflow, it is relatively insensitive to the shape of the inflow profile.
In the presence of significant deep-water inflow through the Yucatan Straits, bottom topography may prevent Loop Current penetration, westward spreading and eddy shedding. In these cases the interaction between the bottom topography and the pressure field near the Florida Shelf results in a near balance between the pressure torques and the nonlinear terms in the mass transport vorticity equation. When the Yucatan Straits deep-water inflow is reduced or the Florida Shelf is moved to the east, the eddy shedding reappears. A kinematic analysis shows that a sufficiently strong current following f/h contours of the Florida Shelf and intersecting the Loop Current at large angles can locally prevent northward penetration of the Loop Current and effectively reduce the port separation. Thus, the effect of the Florida Shelf is similar to cases in the reduced gravity model where the ports are too close for eddy shedding to occur, i.e., when RB>2. Bottom topography also inhibits development of baroclinic instability, yielding solutions more closely resembling those from the reduced gravity model than from the two-layer flat bottom model. However, movement of the shed eddies is significantly modified by the introduction of topography.
In the presence of realistic time variations in the upper layer inflow, the eddy-shedding period is dominated by the natural period rather than the forcing period, although the influence of the latter is not negligible.